1. Field of the Invention
The present patent generally relates to magnetic resonance tomography (or magnetic resonance imaging—MRI), which is used in the medical field for examining patients. The present invention particularly relates to a magnetic resonance imaging device and to a method to operate such device, in which star-shaped streak artifacts, which arise due to radial and/or spiral-type undersampling of k-space, are minimized without simultaneously increasing other factors that contribute to the degradation of the image.
2. Description of the Prior Art
Magnetic resonance imaging is based on the physical phenomena of nuclear spin resonance and has been successfully used in medicine and biophysics for over 15 years. This examination method subjects the object of examination to a strong, constant magnetic field. This exposure aligns the previously randomly oriented nuclear spins in the object. Radio-frequency energy can excite these “ordered” nuclear spins to a certain oscillation. This oscillation produces in the magnetic resonance imaging system the actual signal to be measured, which is received by suitable receiver coils, Using inhomogeneous magnetic fields, generated by gradient coils, the object can be spatially coded in all three directions in space. This method allows one to freely select the layer to be imaged, which means that sectional images of the human body can be recorded in all directions. Magnetic resonance imaging, as a sectional imaging method used in medical diagnostics, is primarily regarded as a non-invasive examination method with versatile contrast capabilities. Due to its outstanding capability to display soft tissue, magnetic resonance imaging has developed into an imaging procedure that is far superior to X-ray computed tomography (CT). Currently, magnetic resonance imaging focuses on the use of spin echo and gradient echo sequences that achieve an excellent image quality with measurement times in the magnitude of minutes.
The continuing technical development of the components of magnetic resonance imaging and the introduction of fast imaging sequences have opened more new fields in medicine to the beneficial use of magnetic resonance imaging. Examples of these applications include real-time imaging to support minimally invasive surgical interventions, functional imaging in neurology, and perfusion measurement in cardiology.
Despite these positive characteristics, magnetic resonance imaging must be characterized as a relatively insensitive imaging technique, because—in spite of the many nuclei in, for example, a human body—the signal-producing nuclear magnetic moment is still very small, Therefore, in practical application it is necessary to find an acceptable compromise between the duration of the measurement and the image quality (resolution and contrast). Particularly in the case of objects to be examined that are moving (e.g., in real-time imaging or in applications for cardiology), a balance must be found between the temporal resolution (motion sharpness) and the image quality. Therefore, in many cases, only a portion of the data that are required for an artifact-free image are recorded, which is generally called “undersampling,” and, ultimately, this results in images with artifacts. The kind of artifact in the resulting image depends on the selected k-space trajectory.
In magnetic resonance imaging, the k-space trajectory defines the data recording, i.e., the sequence of the data acquisition in k-space (frequency domain). The MRI image in the image domain is linked with the MRI data in the k-space by means of the Fourier transformation. The spatial encoding of the object, which spans k-space, occurs by means of gradients that extend in all three directions in space. These directions represent the slice selection (defines a slice in the object to be scanned, usually along the z axis), frequency encoding (defines a direction in the slice, usually along the x axis), and phase encoding (defines the second dimension within the slice, usually along the y axis). Depending on the combination, i.e., switching of the three gradients in the imaging sequence, the scanning of k-space can occur in Cartesian coordinate system (also called linear scanning) or in the cylindrical coordinate system, i.e., spiral scanning.
In order to acquire data for a slice of the object to be examined in the Cartesian system, an imaging sequence for different values of the phase encoding gradient, e.g., Gy, is repeated N times, wherein for each repetition, the frequency of the nuclear resonance signal is scanned, digitized, and stored by a Δt-clocked ADC (analog digital converter) N times in equidistant time steps Δt in the presence of the readout gradient Gx. In this way, a numerical matrix is created line by line (matrix in k-space, also called the k-matrix) with N×N data points (a symmetrical matrix with N×N points is only an example; asymmetrical matrices also can be produced). Using Fourier transformation, an MR image of the scanned slice is reconstructed with a resolution of N×N pixels.
It is also possible to fill (make entries in) k-space by a projection reconstruction procedure, i.e., to fill k-matrix by means of radial scanning, A radial scanning trajectory in k-space includes of sections of the projection (straight) lines through the point of origin of k-space, which form an angle Δφ with each other. Each projection line corresponds to one Fourier-transformed (parallel) projection of the object to be imaged. No phase encoding occurs when the scanning is done using projection lines.
The projection itself exists only in the image domain and is composed of the entirety of all line integrals through the object to be imaged along the defined projection direction. This projection in the image space is reflected by a straight line in k-space—the aforementioned projection line—which intersects its center and is orthogonal to the projection direction. The projection line is first unidirectional, because—from a mathematical point of view—it possesses no preferred direction. The function values on this line—just like in Cartesian scanning—are obtained by Fourier transformation of the projection values. In order to be able to determine, in an MRI procedure, the k-space values pertaining to a projection, the undirectional projection line must be passed and scanned in time, which is achieved by suitable control of the MRI device. Thus, using the measurement process, the projection line acquires a direction. This newly directed line is called the directed projection line.
The directed projection line can once again be divided into an incoming spoke and an outgoing spoke.
Thus, the same projection can be measured with two directed projection lines by reversing the direction of passing, i.e., the incoming and the outgoing spokes are mutually exchanged. Due to physical interference effects—which will be explained in more detail below—the measured function values on the line, i.e., the spoke, depend on the direction of passing. The present invention deals with the minimization of such interference effects with a simultaneous minimal measurement cost, in relation to the entire scanning of the object to be examined with a multitude of projection lines.
During the readout, the data of a projection line, i.e., of a single k-space line, is frequency-encoded by means of a gradient. In the acquisition process for projection reconstruction, a gradient is used that does not scan line-by-line as in the Cartesian system, but rather rotates around the sample. In this manner, in each measurement step the corresponding projection from a certain direction through the entire sample is obtained and thus a typical data set for the projection reconstruction in k-space, as is shown in FIG. 4. Each projection in k-space forms, with each neighbor, an angle Δφ, which is produced by rotating the readout gradient.
Since the image acquisition time increases with the number of the measured k-space lines and in many cases is proportional, most procedures shorten the image acquisition time by the reduction of the number of the measured k-space lines, which is the previously referenced “undersampling”. Such procedures inevitably result in image artifacts. In Cartesian scanning, it is the phase encoding that is reduced; in radial scanning, the number of projection is reduced.
The so-called “aliasing” artifacts predominate in Cartesian scanning, whereas in radial and spiral-type undersampling it is star-like streak artifacts around the objects included in the image that typically occur.
In order to correctly image an object to be examined, it is necessary to acquire data along several projection lines, which usually in combination enclose a constant azimuth angle Δφ, and overall, include an angle range of at least 180°. In the case of (the necessary, because it is time-saving) undersampling (i.e., Δφ>Δφmax, where Δφmax is the angular spacing that must be adhered to if a complete scanning is to be obtained), the above-mentioned streak artifacts occur outside a circular area around the point object defined by a radius (artifact radius) R. This artifact radius R and the amplitude of the streak artifacts represent the essential image quality parameters. They determine the size of the objects that can be imaged (streak-) artifact-free, and—if larger objects must be imaged—how strong the occurring artifacts will be. According to the article “Reduced Circular Field-of-View Imaging, Schefflin et al, J. of Magnetic Resonance in Medicine 40 (1998) 474-480”, equation (5), R is proportional to 1/Δφ, (where, as described above, Δφ represents the azimuthal angular spacing of adjacent projection lines), and thus, by analogy, is proportional to the total number (Nφ) of the scanned projection lines.
Other basic image quality factors, which also produce image artifacts, are “signal decay” and “eddy currents”. For physical reasons (transverse and longitudinal relaxation), signal decay occurs during every scanning; they can manifest themselves differently depending on the type of tissue, the type of scanning of the k-space that is used, and the design of the excitation. With radial scanning of k-space, signal decay can either occur during the scanning of a projection line and manipulate the data of this projection line, or it can manifest itself as a different weighting between the different (adjacent) projection lines and then distort their consistency. Eddy currents are induced in conductive surfaces of the MRI device during the scanning due to the switching of the gradient fields. Such eddy currents decay with different time constants and, during this process, generate different magnetic interference fields, which then cause image interference in the image volume.
The state of the art essentially provides three methods to reduce the above-mentioned streak artifacts:
Scheffler et al (see above) use an angular range of 180° to obtain as large an artifact-free radius (R) as possible with a fixed but low number of projections Nφ, because, in this manner, the azimuthal angular spacing Δφ is minimized. FIG. 2A shows such a 180° k-space scanning. An arrow indicates the direction of scanning of each projection line. In this example, the number of projections is Nφ=10; the angular spacing Δφ is, generally expressed, 180°/Nφ, and thus, in this example, it is Δφ=18°. In this example, the method of scanning k-space is independent of whether the number of projections is even or odd. Nevertheless, with regard to the two other aforementioned image quality factors, such a scanning of k-space results in the following problems: Firstly, the “angular increment” causes the steady state of the eddy currents between the acquisition of the last projection line of the preceding measurement and the first projection line of the subsequent measurement to be interrupted, i.e., stronger eddy-current artifacts occur. Secondly, the signal decays are not compensated for during the scanning process, which results in a strong interference with the acquisition and thus of the image quality.
A second solution is to scan an angular range of 360° with an even number of azimuthally equidistant projections. FIG. 2B illustrates such a scanning system in a simplified manner. Scanning of k-space is performed using an even number of projections Nφ=10 and a 360° scanning range. Similarly as in FIG. 2A, an arrow indicates the scanning of each projection line. The arrow's direction corresponds with the readout direction. Using a simple calculation, the angular increment Δφ is determined to be:
      Δ    ⁢                  ⁢    φ    =                    360        ⁢        °                    N        ⁢                                  ⁢        φ              =          36      ⁢      °      
First, a scanning of this type (an even number of projections) guarantees that the angular increments Δφ between all projection lines are identical. This symmetry results in a steady state with regard to eddy currents, i.e., all projection lines are uniformly influenced by eddy currents, and the eddy current-induced artifacts are very small. Second, due to the even number of projections to each projection line, there exists another projection line that has been acquired in exactly the opposite direction. This circumstance largely compensates for artifacts induced by a signal decay occurring during the acquisition. However, a serious disadvantage of this procedure is that, due to the double measurement (redundancy, see FIG. 2B) of each projection line, the artifacts-free radius R reaches only half of its possible value, so that those parts of the objects that are located farther from each other than R will strongly interfere with each other. In order to correctly represent the object, the number of projections would have to be substantially increased, which would proportionally (and therefore significantly) increase the measurement time.
A third solution is the radially curved procedure described in Barger et al. Time-Resolved Contrast-Enhanced Imaging with Isotropic Resolution and Broad Coverage Using an Undersampled 3D Projection Trajectory, 48, pages 297-305, 2002. As already explained, during a radial scanning procedure, data are recorded on axial straight-line sections. The measurement usually starts outside on the incoming spoke, reaches the center of k-space and continues along the outgoing spoke in the radially curved procedure, after reaching the center the direction is slightly changed. Thus, a measurement (scanning) line arises that is formed by two non-parallel spokes: an incoming spoke and an outgoing spoke. The direction is conveniently changed in such a manner that the outgoing spoke fits in the middle of two incoming spokes. In this way, the radially curved procedure circumvents the described effects (eddy currents and signal decay) by modifying the individual projections: at the point of origin of k-space, the projection lines are curved so that the second halves of the projection lines (outgoing spoke) with angles <180° fall between the first halves of the projection lines (incoming spokes) with angles >180°. However, this procedure has the great disadvantage that, upon reaching the point of origin of k-space, the gradients must be switched, discontinuously and exactly, between two digitization points in order to produce the change in orientation. A clean switchover is especially important, because it is the central, and thus contrast-determining, points of k-space that are particularly involved in this process. The difficulty of an exact switchover increases with an increasing bandwidth per pixel (measurement point in k-space) and with an increasing size of the angular increment. The latter is again proportional to the total number of projections, which means that this solution is difficult to implement in low-resolution real-time applications.